Question

Finding Frequencies, Amplitudes, and Phase Angles. Find a particular solution of the form $y_p = A \cos(\omega t - \phi)$ for each equation in Exercise CHAPTER 4. SECOND-ORDER LINEAR EQUATIONS 267 Group 4.3.5.11-17 and determine the frequency $\omega$, amplitude A, and phase angle $\phi$ of the solution. 11. $y'' + 4y = 3 \cos 2t$ $\frac{d^2x}{dx^2} + \frac{dx}{dt} + 2x = 2 \cos 2t$ 15. $y'' + 6y' + 7y = 3 \sin 2t$ 17. $y'' + 6y' + 8y = \cos 2t$ 12. $y'' + 7y' + 10y = 4 \sin 2t$ Hint. Assume the complex solution has form $y_c = Ae^{3it}$. 14. $x'' - 2x' + 5x = 3 \cos t$ 16. $y'' + 4y' + 13y = 3 \cos 2t$

          Finding Frequencies, Amplitudes, and Phase Angles. Find a particular solution of the form $y_p = A \cos(\omega t - \phi)$ for each equation in Exercise
CHAPTER 4. SECOND-ORDER LINEAR EQUATIONS
267
Group 4.3.5.11-17 and determine the frequency $\omega$, amplitude A, and phase
angle $\phi$ of the solution.
11. $y'' + 4y = 3 \cos 2t$
$\frac{d^2x}{dx^2} + \frac{dx}{dt} + 2x = 2 \cos 2t$
15. $y'' + 6y' + 7y = 3 \sin 2t$
17. $y'' + 6y' + 8y = \cos 2t$
12. $y'' + 7y' + 10y = 4 \sin 2t$
Hint. Assume the complex
solution has form $y_c = Ae^{3it}$.
14. $x'' - 2x' + 5x = 3 \cos t$
16. $y'' + 4y' + 13y = 3 \cos 2t$

Finding Frequencies, Amplitudes, and Phase Angles. Find a particular solution of the form yp = A cos(ω t - ϕ) for each equation in Exercise
CHAPTER 4. SECOND-ORDER LINEAR EQUATIONS
267
Group 4.3.5.11-17 and determine the frequency ω, amplitude A, and phase
angle ϕ of the solution.
11. y” + 4y = 3 cos 2t
(d^2x)/(dx^2) + (dx)/(dt) + 2x = 2 cos 2t
15. y” + 6y' + 7y = 3 sin 2t
17. y” + 6y' + 8y = cos 2t
12. y” + 7y' + 10y = 4 sin 2t
Hint. Assume the complex
solution has form yc = Ae^3it.
14. x” - 2x' + 5x = 3 cos t
16. y” + 4y' + 13y = 3 cos 2t

Added by Scott H.

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